# Relativistic theory of tidal Love numbers

## Abstract

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

- Authors:

- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada) and Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada) and Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, M5S 3H8 (Canada)

- Publication Date:

- OSTI Identifier:
- 21325362

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 80; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.80.084018; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; EQUATIONS OF STATE; GRAVITATION; GRAVITATIONAL WAVE DETECTORS; MASS; NEUTRON STARS; RELATIVISTIC RANGE; SPHERICAL CONFIGURATION

### Citation Formats

```
Binnington, Taylor, and Poisson, Eric.
```*Relativistic theory of tidal Love numbers*. United States: N. p., 2009.
Web. doi:10.1103/PHYSREVD.80.084018.

```
Binnington, Taylor, & Poisson, Eric.
```*Relativistic theory of tidal Love numbers*. United States. doi:10.1103/PHYSREVD.80.084018.

```
Binnington, Taylor, and Poisson, Eric. Thu .
"Relativistic theory of tidal Love numbers". United States. doi:10.1103/PHYSREVD.80.084018.
```

```
@article{osti_21325362,
```

title = {Relativistic theory of tidal Love numbers},

author = {Binnington, Taylor and Poisson, Eric},

abstractNote = {In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.},

doi = {10.1103/PHYSREVD.80.084018},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 8,

volume = 80,

place = {United States},

year = {2009},

month = {10}

}